Could you determine whether the following limit type is indeterminate, always has a fixed finite value, or never has a fixed finite value ? In the first case answer IND, in the second case you can use numerical values, and in the third case answer DNE.
(Note that L'Hospital's rule (in some form) may ONLY be applied to indeterminate forms. )
11. pi^-infty
12. infty/0
13. pi^infty
14. infty*infty
15. infty^1
16. 0^0
17. infty^-infty
18. 1/-infty
19. infty^0
20. 1^0
(Note that L'Hospital's rule (in some form) may ONLY be applied to indeterminate forms. )
11. pi^-infty
12. infty/0
13. pi^infty
14. infty*infty
15. infty^1
16. 0^0
17. infty^-infty
18. 1/-infty
19. infty^0
20. 1^0
-
11) π^(-∞) = 1 ⁄ π^(∞) ... since [π > 1] , then
= 1 ⁄ ∞
= 0
12) (∞ ⁄ 0) = ∞
13) π^(∞) = ∞
14) ∞^(∞) = ∞
15) ∞^(1) = ∞
16) 0^(0) = 0
17) ∞^(-∞) = 1 ⁄ ∞^(∞) = 0
18) 0
19) 1
20) 1
= 1 ⁄ ∞
= 0
12) (∞ ⁄ 0) = ∞
13) π^(∞) = ∞
14) ∞^(∞) = ∞
15) ∞^(1) = ∞
16) 0^(0) = 0
17) ∞^(-∞) = 1 ⁄ ∞^(∞) = 0
18) 0
19) 1
20) 1